G2 Geometry Predicts All Standard Model Parameters: A Zero-Free-Parameter Framework

This preprint presents a theoretical framework in which all Standard Model particle masses, mixing angles, and coupling constants are derived geometrically from a single G2 octonion field undergoing a topological vortex condensation in the early universe. The condensation produces exactly six active vacuum orientations at 60-degree intervals, from which precisely three stable particle loop sizes emerge — corresponding to the three observed generations of matter — with no free parameters beyond the Planck mass. The framework yields over 30 numerical predictions matched against PDG experimental values. Three are independently verifiable with a pocket calculator and are presented on pages 11-12: the proton mass (predicted 939.0 MeV, measured 938.3 MeV, error 0.08%), the neutrino mixing angle theta_13 (predicted pi/21 = 8.571 degrees, measured 8.57 degrees, error 0.02%), and the hydrogen ionisation energy (predicted 13.6057 eV, measured 13.6057 eV, error 0.000%). Additional predictions include new particles accessible to existing LHC searches: a chi familon resonance at 94.6 GeV in the dijet channel, and supersymmetric partners at 391 GeV and 684 GeV. The document is structured in four parts: an accessible introduction with the three verifiable predictions (Part 1, pages 1-14), the physical and geometric foundation (Parts 2 and 3), and the full mathematical derivations with the complete prediction table (Part 4) V3 Added this session: Baryon sector (new — section 4.10.3–4.10.4): Baryon octet mass formula: m² = N_eff · Λ², with N_eff from three ingredients: generation resonance (2^(g₁+g₂−1) per edge), field-amplitude sharing (4/√2 for lone gen-1 among gen-2s), J=3/2 spin coherence (center = 5/4 for Omega) Results: Xi0 +0.04%, Xi− −0.48%, Omega− −0.037%, proton/neutron unchanged, Lambda/Sigma average −0.24% Lambda-Sigma hyperfine: H_HF = (τ₀²/h_dual)·Λ · Σ P_triplet/2^(g₁+g₂−2), gives 74 MeV splitting vs 77.5 MeV, correct sign GE/GM phase: ΔΦ = arctan(Nc/h_dual) = 36.87°, confirmed by BESIII (37° ± 12°) Threshold plateau: FSI overlap mechanism, E_FSI = Λ/2 universal, cross-section ratios σ(p)/σ(Λ) ~ 2/3 7/102 derivation (replaces incomplete APS claim — 5 locations): Source: baryon Z_3 holonomy shifts vacuum by 120°, acts on 7 Fano directions as 1 fixed point + 2 orbits of 3, giving η = −2, diluted by 7/17 over G2 field space and 1/6 over color channels → 7/102 = N_Fano/(2·Nc·(dim_G2+Nc)) Other improvements: Higgs mass 0.60% → 0.071% (A_t from G4 flux) α_s input stated explicitly in 4.5.4 Gravity section 4.13 roadmap with reader's guide Sigma column in prediction tables Open items list updated (5 items, hyperfine added)